The evaluation of aerodynamic drag of go-karts by means of ...

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GMC 2007Cologne, 05-06/11/2007

The evaluation of aerodynamic drag of go-karts by means of

coast down test and CFD analysis



Dr. Marco Evangelos BiancoliniDepartment of Mechanical Engineering

University of Rome Tor Vergata




GMC 2007Cologne, 05-06/11/2007

TVK Research GroupTVK Research Group

The Tor Vergata Karting (TVK) Research Group was born in 2002.Active in the Motorsports field, from competition go-karts to Formulas. Development of multi-disciplinary simulation tools, ranging from structural mechanics and fluid dynamics to vehicle dynamics and innovative materials. Two spin-off companies are going to born

Engineering software tools for the design and optimization of competition go-karts (www.tvk-project.com)Fluid-structure interaction and shape optimization tools to be integrated in the most used CFD software.


GMC 2007Cologne, 05-06/11/2007

Land Speed RecordLand Speed Record

Buckeye Bullet with Ohio state UniversitySuspensionsChassis

Go kart Land Speed Record ProjectDrag evaluation (CFD, coast down test)Mission simulation, sensitivity analysisBodywork optimisation (CFD, wind tunnel testing)


GMC 2007Cologne, 05-06/11/2007

Goals of this studyGoals of this study

Aerodynamic Drag calculation by means of CFD analysisEvaluation of vehicle losses (Drag and Rolling) by means of coast down testLand speed record vehicle mission simulationSensitivity analysis to drive LSR vehicle design and optimisation


GMC 2007Cologne, 05-06/11/2007

CFD AnalysisCFD Analysis

Geometric model TVK 2003Full detailed CFD model in Fluent

Virtual wind tunnelReference speed 90 km/hrGround and wheels speed

Drag forces analysisResultantDistribution on vehicle parts


GMC 2007Cologne, 05-06/11/2007

Geometric modelGeometric model


GMC 2007Cologne, 05-06/11/2007

CFD modelCFD model

Pressure acting on wetted surfacesStream lines of flow field


GMC 2007Cologne, 05-06/11/2007


GMC 2007Cologne, 05-06/11/2007

CFD results: drag forces and down forcesCFD results: drag forces and down forces

Forces on componentsTotal lift: 30NTotal drag: 173NCX calculation

( )

78.0

90

2.1

0.5748421

3

2

2

=

=

=

=

=

x

front

frontxdrag

Chrkmv

mkg

mA

ACvvF

ρ

ρ


GMC 2007Cologne, 05-06/11/2007

CFD result: drag distributionCFD result: drag distribution

Contribution of components to global drag33% driver20% wheels15% front spoiler and deflector10% radiator


GMC 2007Cologne, 05-06/11/2007

CFD results: CX vs speedCFD results: CX vs speed

0.76

0.77

0.78

0.79

0.8

0.81

0.82

50 75 100 125 150

Speed (kph)


GMC 2007Cologne, 05-06/11/2007

Experimental measurement of losses…Experimental measurement of losses…

Go kart: CRG 100 Black Star Engine: Maxter 100 2TCircuit: ISAM AnagniDriver: Gabbiani Jr.Data logger: PI Delta Clubman Kart Kit Technical support: Racing Team CIK, PI Research


GMC 2007Cologne, 05-06/11/2007

…on track.…on track.


GMC 2007Cologne, 05-06/11/2007

Acquisition system detailsAcquisition system details

Data logger PI Delta Clubman, dashboard PI X-Kart, speed sensor mounted on the front wheelRPM sensor coolant temperature sensor.


GMC 2007Cologne, 05-06/11/2007

Acquisition system detailsAcquisition system details

Centrifugal clutchAvoids rear axle locking at high speed in the event of engine failureAllows to disconnect the engine while vehicle is running for the execution of coast down test


GMC 2007Cologne, 05-06/11/2007

Measurement procedure for the evaluation of losses and engine thrust

Measurement procedure for the evaluation of losses and engine thrust

Deceleration data allow losses parameters to be identified.Test is performed disconnecting the engine at high speed along the straight.Acceleration data analysis allows actual thrust at the wheel to be estimated; torque curve can be derived introducing mechanical efficiency of the transmission.Test is performed accelerating the vehicle on the straight until maximum speed is achieved.


GMC 2007Cologne, 05-06/11/2007

Data analysis theoretical modelData analysis theoretical model

Vehicle equation of motion in longitudinal directionThrust is related to dynamic torque delivered by the engine through the transmission ratio and efficiencyRolling losses and aerodynamic drag losses are accountedA model with stabilized constant CX is assumed (applicable for investigated speed range as confirmed by CFD analysis)

( )( )

( ) ( )

( ) frontxdrag

roll

ttotrottotrot

thrust

rolldragthrusttot

tot

ACvvF

vffMgvFZRZR

vTvF

vFvFvFvFMavF

2

10

.

.

21

12

)(

)()()(

ρ

ηπ

=

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−−==


GMC 2007Cologne, 05-06/11/2007

Free decelerationFree deceleration

Observed acceleration and losses are a second order polynomial of speedPolynomial coefficients are related to unknown vehicle losses model parametersA regression algorithm allows to estimate unknown coefficients

( )

⎪⎪

⎩

⎪⎪

⎨

⎧

==

=

⎪⎩

⎪⎨⎧

++=−

++=−

cMgfbMgf

aAC

cbvavMa

ACvvffMgMa

frontx

frontx

0

1

2

210

21

21

ρ

ρ


GMC 2007Cologne, 05-06/11/2007

AccelerationAcceleration

Identified coefficients for losses are introduced in the modelComplete equation is imposed considering observed values of speed and accelerationThe only unknown is the thrustTorque curve is computed

( )( )

( ) ( )

( ) frontxdrag

roll

ttotrottotrot

thrust

rolldragthrusttot

tot

ACvvF

vffMgvFZRZR

vTvF

vFvFvFvFMavF

2

10

.

.

21

12

)(

)()()(

ρ

ηπ

=

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−−==


GMC 2007Cologne, 05-06/11/2007

Results: decelerationResults: deceleration

At each lap a deceleration test is performedThe portion of speed vs time curve recorded related to coast down is extractedRaw data are filtered (median smoothing)Step 1

Acceleration is computed by means of numerical differentiation of filtered dataPolynomial regression

Step 2Results of Step 1 are used as guess valuesLeast squares identification algorithm (integral formulation)


GMC 2007Cologne, 05-06/11/2007

Results for reference vehicle set-upResults for reference vehicle set-up

Comparison between experimental data and identified model

Numerical values of loss model

0 20 40 60 80 100250

200

150

100

50

0PolynomialExperimentalPolynomialExperimental

Speed (kph)

Forc

e (N

)

⎪⎩

⎪⎨

⎧

=⋅−=

=

0.027105.114

899.0

0

4-1

ff

Cx


GMC 2007Cologne, 05-06/11/2007

Results: accelerationResults: acceleration

At each lap an acceleration test is performedThe portion of speed vstime curve recorded related to acceleration test is extractedNumerical differentiation of filtered dataThrust calculationTorque calculation


GMC 2007Cologne, 05-06/11/2007

Thrust and torque curveThrust and torque curve

Resultant of longitudinal force obtained from the acceleration curve

Comparison between estimated torque curve and nominal torque curve provided by Maxter

100

200

300

400

500

600

Long

itudi

nal F

orce

(N)

70 80 90 100 110 120 1300.5

1

1.5

2Estimated from accelerationNominalEstimated from accelerationNominal

Speed (kph)

Torq

ue in

dex


GMC 2007Cologne, 05-06/11/2007

Sensitivity analysisSensitivity analysis

Mathematical model can be used to simulate the mission of LSR to estimate:

Sensitivity of top speed to model parametersAcceleration time and space required to reach top speedPlanning of vehicle improvements toward a new record (current record is 185 km/hr for category investigated in this study)


GMC 2007Cologne, 05-06/11/2007

Top speed calculationTop speed calculation

Theoretical top speed is calculated from equilibrium between engine max power and power lossTransmission ratio for top speed is obtained imposing that at top speed the engine runs at maximum power RPM

( ) vACvvffMgP frontxt ⎟⎠⎞

⎜⎝⎛ ++= 2

10max 21 ρη

max

maxmax

2v

RRPMZ rotP

Vπ

=


GMC 2007Cologne, 05-06/11/2007

Sensitivity analysis resultsSensitivity analysis results

Variation (± 40%) of each parameter (step 20%)Effect (%) on vehicle top speed

-0.35-0.170.170.3Weight

12.36.5-7.4-16.3Power

0.930.46-0.46-0.92f1

-1.27-0.60.6-1.27f0

-10.7-5.97.818.9Cx * Cross section

40%20%-20%-40%


GMC 2007Cologne, 05-06/11/2007

Feasible solutionFeasible solution

Acting on the parameters that mainly influence top speed

Reduction of drag acting on bodyworkIncreasing max power tuning the engine

vmax 0.8 26 hp⋅,( ) 132.616kmhr

=

vmax 0.2 30 hp⋅,( ) 196.61kmhr

=

0 50 100 150 2000

5

10

15

20

25

30ThrustLossesMax

ThrustLossesMax

Power balance

Speed (kph)

Pow

er (k

W)


GMC 2007Cologne, 05-06/11/2007

Feasible solution detailsFeasible solution details

Optimised driver positionRoll bar and safety beltsStreamlined bodywork for reduced dragStabilizer finSuper kart high speed wheels

CFD optimisation for CX reduction (currently 0.2 that could further be reduced)


GMC 2007Cologne, 05-06/11/2007

ConclusionsConclusions

CFD analysis allows to perform a quantitative prediction of aerodynamic drag (Cx=0.78) The proposed experimental test method allows to evaluate loss model parameters (Cx=0.899) and actual engine thrustDifferent estimation can be related to the different set-up (different vehicle shape, different driver heights)CFD analysis allows to study in detail how drag is produced and how is distributed on vehicle componentsMission simulation allows to optimise the project and to plan the eventProposed tools are currently in use to optimise the vehicle (bodywork, engine tuning, tyres)


GMC 2007Cologne, 05-06/11/2007

Top Kart Speed Project is supported by:Top Kart Speed Project is supported by:

Ansys FluentAVL PI ResearchRacing Team CIKISAM proving groundCRG go-kartMAXTER engines


GMC 2007Cologne, 05-06/11/2007









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